Kevin Garnett scored eight of his 26 points in a furious third quarter, and Rajon Rondo finished with 20 points and 13 assists as the Celtics stayed perfect at home this postseason.
With the victory the Celtics took a 3-2 lead in the best-of-seven Eastern Conference series, from which the winner will advance to a meeting with the Detroit Pistons in the conference finals.
Paul Pierce had a team-high 29 points - including eight on free throws in the final 1:23.
Game six will be on Friday in Cleveland, where the Celtics haven't won since 2004.
"We've got some work cut out for us as we go out here on this road and try to close this out, which is the most important thing for us right now," Pierce said.
The Celtics are 0-5 on the road in the playoffs, but have dominated at home.
Cleveland superstar LeBron James looked like he might turn the tables early. He scored 11 points in the first quarter and was up to 23 when a jump shot late in the second quarter stretched the Cavaliers' lead to 43-29.
However James, the five-time All-Star who was 8-of-42 from the floor in the first two games of the series, didn't score again until the final minute of the third quarter.
By then, Garnett and Rondo had taken over.
Rondo, who had made two 3-pointers in a game just once in his career, buried two in a span of 46 seconds to spark a 14-3 scoring run that closed the first half and pulled Boston within 46-43.
"The second quarter - we had a lot more energy," said Garnett, who led all players with 16 rebounds. "Offensively, Rondo hit some big shots, got us going, got us in the flow, and we carried it over to the third quarter."
Little more than a minute into the second half Rondo's steal and layup saw the Celtics take the lead for the first time in the game, and Pierce drained a 3-pointer midway through the third to break a 55-55 tie and put the Celtics ahead for good.
"He was the X-factor tonight," James said. "Rondo played an excellent game. Without Rondo tonight, it would've been a much tighter game. Rondo was the player of the game tonight."
After James' last basket of the first half put the Cavaliers ahead by 14, Boston outscored Cleveland 42-16 in a run spanning more than 15 minutes.
With 3:38 to play Boston led 88-77, but the Cavaliers made the most of two turnovers by the Celtics to close the gap to four points in the final minute.
Garnett missed a jump shot on Boston's next possession, but Ray Allen tipped the miss out to Pierce, who was fouled and made two free throws to make it 93-87 with 15.6 seconds remaining.
After Delonte West hit a pair of free throws for the Cavaliers, Pierce sank two more, and Cleveland's five-second violation with 11 seconds left doomed their comeback bid.
James finished with 35 points but had just four baskets in the second half.
"They came out and turned up their aggression in the third quarter, and that was the difference in the ballgame," said Cavaliers coach Mike Brown. "That set the tone for the Celtics, it set the tone for the crowd and it was a rough go from there."
Facing elimination, Spurs knew Hornets would be trouble
You probably didn't expect this so soon after Team Duncan so convincingly dispatched the Phoenix Suns.
You must be struggling to fully digest the reality that the defending champs can be eliminated in the second round Thursday night on their own floor.
You undoubtedly are still asking -- even after watching San Antonio get walloped in each of its road games in this series -- how the supposed playoff neophytes from New Orleans have shoved the Spurs into such a perilous position.
Yet we're guessing you'll be interested to hear who's not surprised by any of this.
That would be the Spurs.
It used to be the Dallas Mavericks that presented San Antonio's most uncomfortable matchup, as witnessed in the second round back in 2006, when Dallas won a Game 7 in San Antonio in the Spurs' most recent elimination game.
More recently, Phoenix could claim to be the Spurs' fiercest rival, with most of that animus spilling out of the bloody, chippy, unforgettably controversial second-round saga the Spurs and Suns staged.
But that was last season.
No team has caused more unrest in Gregg Popovich's private thoughts this season than these pesky Hornets.
The Spurs surely were less than thrilled to see the Suns in Round 1, especially after going 0-2 in their first two looks at Phoenix after the Shaquille O'Neal trade. They will be grateful to get back to the Western Conference finals at this point -- given that the Spurs have never won a series from 3-2 down -- but won't exactly be celebrating if Kobe Bryant and Pau Gasol are there waiting for them.
That said …
No one has abused San Antonio in 2007-08, regular season and postseason, like New Orleans.
On a Saturday at home in late January, with the Hornets playing on the second night of a back-to-back, the Spurs absorbed a 24-point pounding. Some six weeks later, this time on the road and with neither team having played the previous night, San Antonio lost by 25.
So the Spurs' angst has little to do with their famed inability to win two titles in a row … or win it all in an even year … or get through a Joey Crawford-officiated game without some sort of run-in.
It's pretty much all about New Orleans repeatedly routing them, which is a new experience for the only team out West with unimpeachable championship cred.
Recognition is finally coming to Byron Scott (the newly minted NBA Coach of the Year) and Jeff Bower (who just finished third in voting by his peers for the NBA's Executive of the Year award) for the team they've assembled around imperious Chris Paul, but none of that is news in South Texas.
They're acutely aware down here that the Hornets don't simply rely on Paul's ability to score inside and outside, get to the line more than most little men and get his teammates involved while he's doing all that damage. They know New Orleans' weaponry extends beyond Paul and David West's ability to stretch the floor and bang inside like Tim Duncan.
Lots of us outsiders underestimated how the pieces that snap in so nicely around those two make containing Paul and West so problematic.
Bower has wisely flanked Paul and West with shooters you can't leave (Peja Stojakovic, Jannero Pargo and Morris Peterson) and with a big man (Tyson Chandler) who just keeps heading straight for the rim to open up more space. The Hornets, as a result, almost skunked Dallas because the Mavs didn't make Paul work enough defensively, couldn't deal with West one-on-one and failed to deter New Orleans from swarming Dirk Nowitzki with a punchless supporting cast. They have a 3-2 lead in this series because the Spurs are equally reluctant to expose themselves by frequently double-teaming West and because West has been borderline unstoppable in support of Paul's brilliance at home. This was underlined Tuesday when the other Spurs couldn't make New Orleans pay for its increased focus on Duncan … and when West out-Timmy-ed him in a 38-point, 14-rebound, 5-block masterpiece.
In its two victories at home, San Antonio's trio of primary West defenders -- Kurt Thomas, Fabricio Oberto and Robert Horry -- sufficiently slowed and frustrated West for the Spurs to survive Paul's prowess. You figure there's a good chance it will happen again in Game 6, given that San Antonio's dreadful third quarters seem to be a Bourbon Street-only issue and that you've inevitably heard by now that the home team is a ridiculous 19-1 in the league's four second-round matchups so far.
Yet that would still leave a Game 7 roadie for the Spurs to win Monday night, in the building where they've lost by 19, 18 and 22 points in Games 1, 2 and 5.
There is one silver (and black) lining in that scenario for San Antonio. An unexpected three-day break between Games 6 and 7 would figure to help the older Spurs be at their freshest for the series decider and possibly give the carefree Hornets more time than Scott would prefer to start thinking about the enormity of the moment.
Yet it's also true that West (back) and Chandler (foot) likewise can benefit healthwise from such a gap … and that the gap exposes San Antonio to some brooding about its own ongoing struggles in New Orleans.
Says one veteran scout: "The Hornets play with such a chip on their shoulder. Especially at home. They look like they have no fear of the Spurs."
Which is nothing San Antonio didn't know, long before most of us realized it.